What do you mean by non-judgmental? Every person on the planet is judgmental. Your thread involves judging various churches. Wouldn't that make you judgmental?
Are there certain features or ministries you want? Married couples, children, mens' ministry, etc?
I'm assuming by AA you mean Alcoholics Anonymous? No one is going to "judge" a former alcoholic as churches are full of people with former substance abuse issues. No one should have a problem with you wife being Jewish as any smart person knows that Christianity was birth out of Judaism.
The thing with being a church member is that you cannot go to church and expect the members to be perfect. People are not perfect and Christians are not perfect. Christianity is a journey to become more Christ-like. Different people are at different stages along their journey. You can't be deterred by someone who is still "rough around the edges."
I don't know what part of town you want to visit but you could look into
City Church.